Subgroups — #20264899

Order 6464.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#11717579	C₂	1	1	yes	maximal, characteristic
2	C₄×#11717579	C₂	1	1	yes	maximal, characteristic
3	C₄×C₈×C₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#11717579	C₄	1	2	yes	—
5	C₂×#11717579	C₄	1	2	yes	—
6	C₂×C₈×C₁₀₁	C₄	1	2	yes	—
7	C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
9	C₂×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
10	C₂×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
11	C₈×C₁₀₁	—	2	2	no	—
12	#11717579	—	2	2	no	—
13	#11717579	C₈	1	4	yes	complemented
14	C₂²×C₁₀₁	C₄²	1	1	yes	characteristic
15	C₄×C₁₀₁	C₂×C₈	1	2	yes	—
16	C₄×C₁₀₁	M₁₆	1	2	yes	—
17	C₄×C₁₀₁	M₁₆	1	2	yes	—
18	C₂×C₁₀₁	C₄×C₈	1	1	yes	characteristic
19	C₂×C₁₀₁	#97	1	1	yes	characteristic
20	C₂×C₁₀₁	#97	1	1	yes	characteristic
21	C₁₀₁	#322	1	1	yes	characteristic, complemented, Sylow
22	#322	—	101	1	no	maximal, Sylow
23	C₄×C₈	—	101	1	no	—
24	C₄×C₈	—	101	1	no	—
25	C₄×C₈	D₁₀₁	1	1	yes	characteristic
26	C₂×C₈	—	101	2	no	—
27	C₂×C₈	—	101	2	no	—
28	C₂×C₈	Dic₁₀₁	1	2	yes	—
29	C₄²	C₂×D₁₀₁	1	1	yes	characteristic
30	C₂×C₄	C₄×D₁₀₁	1	1	yes	characteristic
31	C₂×C₄	C₄×D₁₀₁	1	1	yes	characteristic
32	C₂×C₄	C₂×Dic₁₀₁	1	1	yes	characteristic
33	C₈	—	2	2	no	—
34	C₈	—	101	4	no	—
35	C₈	—	202	2	no	—
36	C₂²	C₄×Dic₁₀₁	1	1	yes	characteristic
37	C₄	C₈×D₁₀₁	1	2	yes	—
38	C₄	#13108057	1	2	yes	—
39	C₄	#13108058	1	2	yes	—
40	C₂	C₈×Dic₁₀₁	1	1	yes	characteristic
41	C₂	#15692165	1	1	yes	characteristic
42	C₂	#15692166	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂×D₁₀₁
commutator	C₂×C₁₀₁	C₄×C₈
Fitting	C₄×C₈×C₁₀₁	C₂
socle	C₂²×C₁₀₁	C₄²
hypercenter	C₄×C₈	D₁₀₁
hypocenter	C₁₀₁	#322
LCS	G ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₄² ◁ C₄×C₈

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
13. #11717579	C₈	semidirect
21. C₁₀₁	#322	semidirect